We propose an extension of the photon soul theorem to higher-dimensional geometries where the electromagnetic field acquires novel topological couplings to the Higgs sector. In four-dimensional spacetime, electroweak symmetry breaking leaves the photon massless and its cohomological soul invariant. We demonstrate that in a D > 4 bulk or derived-stack context, nontrivial morphisms in the derived category of sheaves can induce Higgs–photon soul deformations that vanish under naive dimensional reduction but leave calculable imprints on low-energy interference phenomena. We provide precise cohomological constructions, compute obstruction classes, and derive phenomenological bounds on measurable visibility shifts.